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# Aggregation of individual demand to total, or market, demand

The demand for various commodities by individuals is generally thought of as the outcome of a utility-maximizing process. The interpretation of this relationship between price and quantity demanded of a given good is that, given all the other goods and constraints, this set of choices is that one which makes the consumer happiest.

Aggregate, or market, demand curves represent the sum of these individual demand curves. An important question is whether market demand curves can also be thought of as being generated by a utility-maximization process. Does the aggregated demand curve show how to optimise the total utility (happiness) of society? Does it show how to optimise something else? The answer to these questions is no; market demand curves generally have no utility interpretation.

Moreover, even if market demand curves could mathematically be rationalized by a utility function; they still cannot be economically rationalized as generating an overall welfare index. There are several reasons for this

1. Each person's individual total utility gleaned from purchases depends on the size of her budget, but the distribution of wealth (and thus her budget) is a separate (free) variable in the aggregation. In other words, changing the distribution of wealth (such as giving needy people more resources) will produce a different total for society's utility.
2. Each person's demand curve is a function of her budget, so that if the distribution of wealth changes (by changing the distribution of prices and thus salaries, and so on), all of the individual demand curves change. The aggregate effect of such a change is not simple unless all the consumers have wealth-independent consumption patterns --- that is, unless the pauper and the billionaire spend the same fraction of their budgets on each item.

Markets cannot be claimed to select an optimum in the sense of the greatest total utility of society; indeed, there is not even general agreement on how total utility should be defined. However, under strictly competitive conditions, market outcomes do represent a Pareto optimum.

It has been known since at least 1953 (Gorman, W.M., Community Preference Fields, Econometrica, 21: 63-80) and 1982 (Shafer, W. and Sonnenschein, H., Market demand and excess demand functions, in K. J. Arrow and M. D. Intriligator (eds), Handbook of Mathematical Economics (Vol. II), North-Holland, Amsterdam) that no reasonable assumptions can circumvent these problems.

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03-10-2013 05:06:04